LMFDB - Embedded newform 891.2.bb.a.413.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(8,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(90)) chi = DirichletCharacter(H, H._module([5, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.bb (of order $90$, degree $24$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			413.20
Character	$\chi$	$=$	891.413
Dual form			891.2.bb.a.233.20

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.537360 - 0.0755211i) q^{2} +(-1.63947 + 0.470111i) q^{4} +(-3.32873 + 1.34490i) q^{5} +(0.885188 + 0.597067i) q^{7} +(-1.83694 + 0.817857i) q^{8} +(-1.68716 + 0.974083i) q^{10} +(-1.29032 - 3.05533i) q^{11} +(1.23652 + 2.32555i) q^{13} +(0.520756 + 0.253990i) q^{14} +(1.96743 - 1.22939i) q^{16} +(1.71802 - 0.365177i) q^{17} +(-0.0216751 - 0.0486831i) q^{19} +(4.82511 - 3.76979i) q^{20} +(-0.924110 - 1.54437i) q^{22} +(2.86915 - 7.88293i) q^{23} +(5.67502 - 5.48030i) q^{25} +(0.840084 + 1.15628i) q^{26} +(-1.73193 - 0.562737i) q^{28} +(-3.86018 - 7.91454i) q^{29} +(-0.0700374 + 2.00561i) q^{31} +(4.04507 - 3.39421i) q^{32} +(0.895619 - 0.325979i) q^{34} +(-3.74955 - 0.796991i) q^{35} +(-3.34485 - 1.48922i) q^{37} +(-0.0153239 - 0.0245234i) q^{38} +(5.01474 - 5.19292i) q^{40} +(-4.76416 + 9.76798i) q^{41} +(6.03712 - 7.19476i) q^{43} +(3.55179 + 4.40254i) q^{44} +(0.946441 - 4.45265i) q^{46} +(0.158533 - 0.552870i) q^{47} +(-2.19518 - 5.43326i) q^{49} +(2.63565 - 3.37348i) q^{50} +(-3.12050 - 3.23138i) q^{52} +(-0.862436 + 0.280222i) q^{53} +(8.40424 + 8.43504i) q^{55} +(-2.11435 - 0.372817i) q^{56} +(-2.67202 - 3.96143i) q^{58} +(7.68590 + 1.91631i) q^{59} +(10.3949 - 0.362997i) q^{61} +(0.113830 + 1.08302i) q^{62} +(-1.18738 + 1.31871i) q^{64} +(-7.24367 - 6.07816i) q^{65} +(-0.424053 - 2.40492i) q^{67} +(-2.64498 + 1.40636i) q^{68} +(-2.07505 - 0.145101i) q^{70} +(-0.524273 - 2.46651i) q^{71} +(-9.10036 + 0.956486i) q^{73} +(-1.90986 - 0.547642i) q^{74} +(0.0584222 + 0.0696248i) q^{76} +(0.682061 - 3.47495i) q^{77} +(-0.309973 - 2.20558i) q^{79} +(-4.89565 + 6.73828i) q^{80} +(-1.82238 + 5.60872i) q^{82} +(-8.66574 - 4.60765i) q^{83} +(-5.22772 + 3.52614i) q^{85} +(2.70075 - 4.32211i) q^{86} +(4.86907 + 4.55716i) q^{88} +(8.64475 + 4.99105i) q^{89} +(-0.293959 + 2.79684i) q^{91} +(-0.998041 + 14.2727i) q^{92} +(0.0434360 - 0.309063i) q^{94} +(0.137624 + 0.132902i) q^{95} +(-2.43238 + 6.02035i) q^{97} +(-1.58993 - 2.75383i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.537360	−	0.0755211i	0.379971	−	0.0534014i	0.0533977	−	0.998573i	$-0.482995\pi$
$2$	0.537360	−	0.0755211i	0.379971	−	0.0534014i	0.326573	+	0.945172i	$0.394106\pi$
$3$		0			0
$3$		0			0
$4$	−1.63947	+	0.470111i	−0.819735	+	0.235055i
$5$	−3.32873	+	1.34490i	−1.48865	+	0.601456i	−0.967695	−	0.252125i	$-0.918870\pi$
$5$	−3.32873	+	1.34490i	−1.48865	+	0.601456i	−0.520960	+	0.853581i	$0.674426\pi$
$6$		0			0
$7$	0.885188	+	0.597067i	0.334569	+	0.225670i	0.714975	−	0.699150i	$-0.246438\pi$
$7$	0.885188	+	0.597067i	0.334569	+	0.225670i	−0.380406	+	0.924820i	$0.624216\pi$
$8$	−1.83694	+	0.817857i	−0.649456	+	0.289156i
$9$		0			0
$10$	−1.68716	+	0.974083i	−0.533527	+	0.308032i
$11$	−1.29032	−	3.05533i	−0.389047	−	0.921218i
$11$	−1.29032	−	3.05533i	−0.389047	−	0.921218i
$12$		0			0
$13$	1.23652	+	2.32555i	0.342949	+	0.644993i	0.993419	−	0.114539i	$-0.0365392\pi$
$13$	1.23652	+	2.32555i	0.342949	+	0.644993i	−0.650470	+	0.759532i	$0.725428\pi$
$14$	0.520756	+	0.253990i	0.139178	+	0.0678816i
$15$		0			0
$16$	1.96743	−	1.22939i	0.491857	−	0.307347i
$17$	1.71802	−	0.365177i	0.416682	−	0.0885685i	0.00520025	−	0.999986i	$-0.498345\pi$
$17$	1.71802	−	0.365177i	0.416682	−	0.0885685i	0.411482	+	0.911418i	$0.365011\pi$
$18$		0			0
$19$	−0.0216751	−	0.0486831i	−0.00497261	−	0.0111687i	0.911042	−	0.412313i	$-0.135279\pi$
$19$	−0.0216751	−	0.0486831i	−0.00497261	−	0.0111687i	−0.916015	+	0.401145i	$0.868612\pi$
$20$	4.82511	−	3.76979i	1.07893	−	0.842951i
$21$		0			0
$22$	−0.924110	−	1.54437i	−0.197021	−	0.329261i
$23$	2.86915	−	7.88293i	0.598260	−	1.64370i	−0.156481	−	0.987681i	$-0.550015\pi$
$23$	2.86915	−	7.88293i	0.598260	−	1.64370i	0.754740	−	0.656024i	$-0.227763\pi$
$24$		0			0
$25$	5.67502	−	5.48030i	1.13500	−	1.09606i
$26$	0.840084	+	1.15628i	0.164754	+	0.226765i
$27$		0			0
$28$	−1.73193	−	0.562737i	−0.327303	−	0.106347i
$29$	−3.86018	−	7.91454i	−0.716817	−	1.46969i	−0.875933	−	0.482433i	$-0.839753\pi$
$29$	−3.86018	−	7.91454i	−0.716817	−	1.46969i	0.159115	−	0.987260i	$-0.449136\pi$
$30$		0			0
$31$	−0.0700374	+	2.00561i	−0.0125791	+	0.360218i	0.976738	+	0.214437i	$0.0687917\pi$
$31$	−0.0700374	+	2.00561i	−0.0125791	+	0.360218i	−0.989317	+	0.145781i	$0.953431\pi$
$32$	4.04507	−	3.39421i	0.715073	−	0.600018i
$33$		0			0
$34$	0.895619	−	0.325979i	0.153597	−	0.0559049i
$35$	−3.74955	−	0.796991i	−0.633789	−	0.134716i
$36$		0			0
$37$	−3.34485	−	1.48922i	−0.549889	−	0.244827i	0.112934	−	0.993603i	$-0.463975\pi$
$37$	−3.34485	−	1.48922i	−0.549889	−	0.244827i	−0.662823	+	0.748776i	$0.730642\pi$
$38$	−0.0153239	−	0.0245234i	−0.00248587	−	0.00397823i
$39$		0			0
$40$	5.01474	−	5.19292i	0.792901	−	0.821073i
$41$	−4.76416	+	9.76798i	−0.744037	+	1.52550i	0.103420	+	0.994638i	$0.467021\pi$
$41$	−4.76416	+	9.76798i	−0.744037	+	1.52550i	−0.847457	+	0.530864i	$0.821868\pi$
$42$		0			0
$43$	6.03712	−	7.19476i	0.920652	−	1.09719i	−0.0743399	−	0.997233i	$-0.523685\pi$
$43$	6.03712	−	7.19476i	0.920652	−	1.09719i	0.994992	−	0.0999572i	$-0.0318706\pi$
$44$	3.55179	+	4.40254i	0.535453	+	0.663707i
$45$		0			0
$46$	0.946441	−	4.45265i	0.139545	−	0.656508i
$47$	0.158533	−	0.552870i	0.0231244	−	0.0806444i	−0.948853	−	0.315717i	$-0.897755\pi$
$47$	0.158533	−	0.552870i	0.0231244	−	0.0806444i	0.971978	+	0.235073i	$0.0755328\pi$
$48$		0			0
$49$	−2.19518	−	5.43326i	−0.313597	−	0.776179i
$50$	2.63565	−	3.37348i	0.372738	−	0.477082i
$51$		0			0
$52$	−3.12050	−	3.23138i	−0.432736	−	0.448111i
$53$	−0.862436	+	0.280222i	−0.118465	+	0.0384915i	−0.367649	−	0.929964i	$-0.619837\pi$
$53$	−0.862436	+	0.280222i	−0.118465	+	0.0384915i	0.249185	+	0.968456i	$0.419837\pi$
$54$		0			0
$55$	8.40424	+	8.43504i	1.13323	+	1.13738i
$56$	−2.11435	−	0.372817i	−0.282542	−	0.0498198i
$57$		0			0
$58$	−2.67202	−	3.96143i	−0.350854	−	0.520162i
$59$	7.68590	+	1.91631i	1.00062	+	0.249482i	0.707591	−	0.706622i	$-0.249782\pi$
$59$	7.68590	+	1.91631i	1.00062	+	0.249482i	0.293027	+	0.956104i	$0.405337\pi$
$60$		0			0
$61$	10.3949	−	0.362997i	1.33093	−	0.0464770i	0.639427	−	0.768852i	$-0.279172\pi$
$61$	10.3949	−	0.362997i	1.33093	−	0.0464770i	0.691501	+	0.722375i	$0.256950\pi$
$62$	0.113830	+	1.08302i	0.0144565	+	0.137544i
$63$		0			0
$64$	−1.18738	+	1.31871i	−0.148422	+	0.164839i
$65$	−7.24367	−	6.07816i	−0.898466	−	0.753903i
$66$		0			0
$67$	−0.424053	−	2.40492i	−0.0518063	−	0.293808i	0.947886	−	0.318609i	$-0.103216\pi$
$67$	−0.424053	−	2.40492i	−0.0518063	−	0.293808i	−0.999692	+	0.0248014i	$0.992105\pi$
$68$	−2.64498	+	1.40636i	−0.320751	+	0.170546i
$69$		0			0
$70$	−2.07505	−	0.145101i	−0.248015	−	0.0173429i
$71$	−0.524273	−	2.46651i	−0.0622197	−	0.292721i	0.936026	−	0.351931i	$-0.114475\pi$
$71$	−0.524273	−	2.46651i	−0.0622197	−	0.292721i	−0.998246	+	0.0592107i	$0.981142\pi$
$72$		0			0
$73$	−9.10036	+	0.956486i	−1.06512	+	0.111948i	−0.620837	−	0.783940i	$-0.713207\pi$
$73$	−9.10036	+	0.956486i	−1.06512	+	0.111948i	−0.444279	+	0.895888i	$0.646540\pi$
$74$	−1.90986	−	0.547642i	−0.222016	−	0.0636621i
$75$		0			0
$76$	0.0584222	+	0.0696248i	0.00670148	+	0.00798652i
$77$	0.682061	−	3.47495i	0.0777281	−	0.396008i
$78$		0			0
$79$	−0.309973	−	2.20558i	−0.0348747	−	0.248147i	0.965027	−	0.262150i	$-0.0844314\pi$
$79$	−0.309973	−	2.20558i	−0.0348747	−	0.248147i	−0.999902	+	0.0140031i	$0.995543\pi$
$80$	−4.89565	+	6.73828i	−0.547350	+	0.753363i
$81$		0			0
$82$	−1.82238	+	5.60872i	−0.201248	+	0.619379i
$83$	−8.66574	−	4.60765i	−0.951188	−	0.505756i	−0.0800484	−	0.996791i	$-0.525508\pi$
$83$	−8.66574	−	4.60765i	−0.951188	−	0.505756i	−0.871140	+	0.491035i	$0.836619\pi$
$84$		0			0
$85$	−5.22772	+	3.52614i	−0.567026	+	0.382464i
$86$	2.70075	−	4.32211i	0.291229	−	0.466065i
$87$		0			0
$88$	4.86907	+	4.55716i	0.519045	+	0.485795i
$89$	8.64475	+	4.99105i	0.916342	+	0.529050i	0.882466	−	0.470376i	$-0.155882\pi$
$89$	8.64475	+	4.99105i	0.916342	+	0.529050i	0.0338757	+	0.999426i	$0.489215\pi$
$90$		0			0
$91$	−0.293959	+	2.79684i	−0.0308153	+	0.293188i
$92$	−0.998041	+	14.2727i	−0.104053	+	1.48803i
$93$		0			0
$94$	0.0434360	−	0.309063i	0.00448008	−	0.0318774i
$95$	0.137624	+	0.132902i	0.0141200	+	0.0136355i
$96$		0			0
$97$	−2.43238	+	6.02035i	−0.246971	+	0.611274i	−0.998846	−	0.0480316i	$-0.984705\pi$
$97$	−2.43238	+	6.02035i	−0.246971	+	0.611274i	0.751875	+	0.659306i	$0.229150\pi$
$98$	−1.58993	−	2.75383i	−0.160607	−	0.278179i
$99$		0			0
$100$	−6.72768	+	11.6527i	−0.672768	+	1.16527i
$101$	0.734644	+	0.940301i	0.0730998	+	0.0935634i	0.823171	−	0.567794i	$-0.192203\pi$
$101$	0.734644	+	0.940301i	0.0730998	+	0.0935634i	−0.750071	+	0.661357i	$0.769981\pi$
$102$		0			0
$103$	1.72740	−	6.92824i	0.170206	−	0.682659i	−0.823174	−	0.567789i	$-0.807799\pi$
$103$	1.72740	−	6.92824i	0.170206	−	0.682659i	0.993380	−	0.114871i	$-0.0366454\pi$
$104$	−4.17338	−	3.26060i	−0.409234	−	0.319728i
$105$		0			0
$106$	−0.442276	+	0.215712i	−0.0429576	+	0.0209518i
$107$	−12.8871	−	9.36302i	−1.24584	−	0.905157i	−0.247869	−	0.968794i	$-0.579730\pi$
$107$	−12.8871	−	9.36302i	−1.24584	−	0.905157i	−0.997973	+	0.0636360i	$0.979730\pi$
$108$		0			0
$109$		−	18.9567i		−	1.81572i	−0.419274	−	0.907860i	$-0.637715\pi$
$109$		−	18.9567i		−	1.81572i	0.419274	−	0.907860i	$-0.362285\pi$
$110$	5.15313	+	3.89796i	0.491332	+	0.371656i
$111$		0			0
$112$	2.47557	+	0.0864488i	0.233919	+	0.00816864i
$113$	0.328978	+	4.70461i	0.0309477	+	0.442573i	0.988185	+	0.153268i	$0.0489797\pi$
$113$	0.328978	+	4.70461i	0.0309477	+	0.442573i	−0.957237	+	0.289305i	$0.906576\pi$
$114$		0			0
$115$	1.05108	+	30.0989i	0.0980134	+	2.80674i
$116$	10.0494	+	11.1609i	0.933060	+	1.03627i
$117$		0			0
$118$	4.27482	+	0.449301i	0.393529	+	0.0413615i
$119$	1.73881	+	0.702524i	0.159396	+	0.0644003i
$120$		0			0
$121$	−7.67014	+	7.88473i	−0.697285	+	0.716794i
$122$	5.55838	−	0.980093i	0.503232	−	0.0887334i
$123$		0			0
$124$	−0.828034	−	3.32106i	−0.0743596	−	0.298240i
$125$	−4.21896	+	9.47594i	−0.377355	+	0.847554i
$126$		0			0
$127$	1.24087	−	1.11729i	0.110110	−	0.0991432i	−0.612237	−	0.790674i	$-0.709730\pi$
$127$	1.24087	−	1.11729i	0.110110	−	0.0991432i	0.722347	+	0.691531i	$0.243064\pi$
$128$	−6.44405	+	9.55369i	−0.569579	+	0.844435i
$129$		0			0
$130$	−4.35149	−	2.71911i	−0.381651	−	0.238482i
$131$	7.54127	+	2.74480i	0.658884	+	0.239814i	0.649754	−	0.760144i	$-0.274872\pi$
$131$	7.54127	+	2.74480i	0.658884	+	0.239814i	0.00912929	+	0.999958i	$0.497094\pi$
$132$		0			0
$133$	0.00988051	−	0.0560352i	0.000856749	−	0.00485887i
$134$	−0.409491	−	1.26028i	−0.0353747	−	0.108872i
$135$		0			0
$136$	−2.85724	+	2.07591i	−0.245006	+	0.178008i
$137$	−8.43317	+	15.8605i	−0.720495	+	1.35505i	0.205928	+	0.978567i	$0.433979\pi$
$137$	−8.43317	+	15.8605i	−0.720495	+	1.35505i	−0.926422	+	0.376486i	$0.877132\pi$
$138$		0			0
$139$	−5.66023	−	19.7396i	−0.480094	−	1.67429i	−0.712502	−	0.701670i	$-0.752438\pi$
$139$	−5.66023	−	19.7396i	−0.480094	−	1.67429i	0.232408	−	0.972618i	$-0.425340\pi$
$140$	6.52194	−	0.456059i	0.551205	−	0.0385440i
$141$		0			0
$142$	−0.467997	−	1.28581i	−0.0392734	−	0.107903i
$143$	5.50984	−	6.77869i	0.460756	−	0.566863i
$144$		0			0
$145$	23.4937	+	21.1539i	1.95105	+	1.75673i
$146$	−4.81793	+	1.20125i	−0.398735	+	0.0994158i
$147$		0			0
$148$	6.18388	+	0.869087i	0.508312	+	0.0714385i
$149$	1.81971	+	0.255743i	0.149076	+	0.0209513i	0.213316	−	0.976983i	$-0.431573\pi$
$149$	1.81971	+	0.255743i	0.149076	+	0.0209513i	−0.0642402	+	0.997934i	$0.520462\pi$
$150$		0			0
$151$	−5.66721	+	1.41300i	−0.461191	+	0.114988i	−0.465586	−	0.885002i	$-0.654157\pi$
$151$	−5.66721	+	1.41300i	−0.461191	+	0.114988i	0.00439507	+	0.999990i	$0.498601\pi$
$152$	0.0796317	+	0.0717007i	0.00645898	+	0.00581569i
$153$		0			0
$154$	0.104080	−	1.91881i	0.00838703	−	0.154622i
$155$	−2.46420	−	6.77033i	−0.197929	−	0.543806i
$156$		0			0
$157$	−16.2641	+	1.13730i	−1.29802	+	0.0907662i	−0.701984	−	0.712193i	$-0.747702\pi$
$157$	−16.2641	+	1.13730i	−1.29802	+	0.0907662i	−0.596034	+	0.802959i	$0.703258\pi$
$158$	−0.333135	−	1.16178i	−0.0265028	−	0.0924262i
$159$		0			0
$160$	−8.90008	+	16.7386i	−0.703613	+	1.32330i
$161$	7.24637	−	5.26480i	0.571094	−	0.414924i
$162$		0			0
$163$	−2.58005	−	7.94058i	−0.202085	−	0.621954i	−0.999820	−	0.0189466i	$-0.993969\pi$
$163$	−2.58005	−	7.94058i	−0.202085	−	0.621954i	0.797735	−	0.603008i	$-0.206031\pi$
$164$	3.21867	−	18.2540i	0.251336	−	1.42540i
$165$		0			0
$166$	−5.00460	−	1.82152i	−0.388432	−	0.141378i
$167$	−3.38595	−	2.11578i	−0.262013	−	0.163724i	0.392552	−	0.919730i	$-0.371592\pi$
$167$	−3.38595	−	2.11578i	−0.262013	−	0.163724i	−0.654565	+	0.756006i	$0.727148\pi$
$168$		0			0
$169$	3.39029	−	5.02631i	0.260791	−	0.386639i
$170$	−2.54287	+	2.28961i	−0.195029	+	0.175605i
$171$		0			0
$172$	−6.51535	+	14.6337i	−0.496790	+	1.11581i
$173$	−4.20044	−	16.8470i	−0.319353	−	1.28086i	−0.888597	−	0.458688i	$-0.848320\pi$
$173$	−4.20044	−	16.8470i	−0.319353	−	1.28086i	0.569244	−	0.822169i	$-0.307236\pi$
$174$		0			0
$175$	8.29557	−	1.46273i	0.627086	−	0.110572i
$176$	−6.29480	−	4.42485i	−0.474489	−	0.333536i
$177$		0			0
$178$	5.02228	+	2.02913i	0.376435	+	0.152090i
$179$	12.0443	+	1.26591i	0.900235	+	0.0946185i	0.543327	−	0.839521i	$-0.317164\pi$
$179$	12.0443	+	1.26591i	0.900235	+	0.0946185i	0.356908	+	0.934140i	$0.383831\pi$
$180$		0			0
$181$	−3.91374	−	4.34664i	−0.290906	−	0.323084i	0.579922	−	0.814672i	$-0.303083\pi$
$181$	−3.91374	−	4.34664i	−0.290906	−	0.323084i	−0.870828	+	0.491589i	$0.836416\pi$
$182$	0.0532580	+	1.52511i	0.00394774	+	0.113049i
$183$		0			0
$184$	1.17666	+	16.8270i	0.0867445	+	1.24050i
$185$	13.1370	+	0.458752i	0.965848	+	0.0337282i
$186$		0			0
$187$	−3.33254	−	4.77794i	−0.243700	−	0.349398i
$188$			0.980943i			0.0715426i
$189$		0			0
$190$	0.0839908	+	0.0610229i	0.00609333	+	0.00442706i
$191$	4.59762	−	2.24241i	0.332672	−	0.162255i	−0.264463	−	0.964396i	$-0.585195\pi$
$191$	4.59762	−	2.24241i	0.332672	−	0.162255i	0.597135	+	0.802141i	$0.296306\pi$
$192$		0			0
$193$	15.1350	+	11.8247i	1.08944	+	0.851164i	0.989601	−	0.143840i	$-0.0459450\pi$
$193$	15.1350	+	11.8247i	1.08944	+	0.851164i	0.0998389	+	0.995004i	$0.468167\pi$
$194$	−0.852401	+	3.41879i	−0.0611988	+	0.245455i
$195$		0			0
$196$	6.15316	+	7.87569i	0.439511	+	0.562549i
$197$	5.18853	−	8.98679i	0.369667	−	0.640282i	−0.619846	−	0.784723i	$-0.712805\pi$
$197$	5.18853	−	8.98679i	0.369667	−	0.640282i	0.989513	+	0.144441i	$0.0461384\pi$
$198$		0			0
$199$	−13.1963	−	22.8567i	−0.935463	−	1.62027i	−0.773806	−	0.633423i	$-0.781649\pi$
$199$	−13.1963	−	22.8567i	−0.935463	−	1.62027i	−0.161658	−	0.986847i	$-0.551684\pi$
$200$	−5.94255	+	14.7083i	−0.420202	+	1.04004i
$201$		0			0
$202$	0.465781	+	0.449799i	0.0327722	+	0.0316478i
$203$	1.30852	−	9.31064i	0.0918404	−	0.653479i
$204$		0			0
$205$	2.72171	−	38.9223i	0.190093	−	2.71845i
$206$	0.405010	−	3.85341i	0.0282184	−	0.268480i
$207$		0			0
$208$	5.29177	+	3.05520i	0.366918	+	0.211840i
$209$	−0.120775	+	0.129042i	−0.00835420	+	0.00892600i
$210$		0			0
$211$	0.199344	−	0.319016i	0.0137234	−	0.0219620i	−0.841115	−	0.540856i	$-0.818100\pi$
$211$	0.199344	−	0.319016i	0.0137234	−	0.0219620i	0.854839	+	0.518894i	$0.173656\pi$
$212$	1.28220	−	0.864857i	0.0880621	−	0.0593986i
$213$		0			0
$214$	−7.63212	−	4.05807i	−0.521721	−	0.277404i
$215$	−10.4198	+	32.0687i	−0.710622	+	2.18707i
$216$		0			0
$217$	−1.25948	+	1.73352i	−0.0854989	+	0.117679i
$218$	−1.43163	−	10.1866i	−0.0969621	−	0.689921i
$219$		0			0
$220$	−17.7439	−	9.87808i	−1.19629	−	0.665980i
$221$	2.97361	+	3.54381i	0.200027	+	0.238382i
$222$		0			0
$223$	0.0426395	+	0.0122267i	0.00285535	+	0.000818760i	0.277065	−	0.960851i	$-0.410638\pi$
$223$	0.0426395	+	0.0122267i	0.00285535	+	0.000818760i	−0.274209	+	0.961670i	$0.588416\pi$
$224$	5.60721	−	0.589342i	0.374648	−	0.0393771i
$225$		0			0
$226$	0.532077	+	2.50323i	0.0353932	+	0.166512i
$227$	8.44001	+	0.590183i	0.560183	+	0.0391718i	0.347042	−	0.937850i	$-0.387186\pi$
$227$	8.44001	+	0.590183i	0.560183	+	0.0391718i	0.213141	+	0.977021i	$0.431631\pi$
$228$		0			0
$229$	8.00867	−	4.25828i	0.529228	−	0.281395i	−0.183279	−	0.983061i	$-0.558671\pi$
$229$	8.00867	−	4.25828i	0.529228	−	0.281395i	0.712506	+	0.701666i	$0.247560\pi$
$230$	2.83791	+	16.0946i	0.187126	+	1.06124i
$231$		0			0
$232$	13.5639	+	11.3814i	0.890512	+	0.747228i
$233$	−7.83982	+	8.70700i	−0.513604	+	0.570415i	−0.943039	−	0.332683i	$-0.892046\pi$
$233$	−7.83982	+	8.70700i	−0.513604	+	0.570415i	0.429435	+	0.903098i	$0.358713\pi$
$234$		0			0
$235$	0.215839	+	2.05357i	0.0140798	+	0.133960i
$236$	−13.5017	+	0.471489i	−0.878884	+	0.0306913i
$237$		0			0
$238$	0.987422	+	0.246192i	0.0640051	+	0.0159583i
$239$	9.41880	+	13.9639i	0.609251	+	0.903252i	0.999850	−	0.0173086i	$-0.00550978\pi$
$239$	9.41880	+	13.9639i	0.609251	+	0.903252i	−0.390599	+	0.920561i	$0.627732\pi$
$240$		0			0
$241$	−4.18318	−	0.737607i	−0.269462	−	0.0475134i	0.0372844	−	0.999305i	$-0.488129\pi$
$241$	−4.18318	−	0.737607i	−0.269462	−	0.0475134i	−0.306746	+	0.951791i	$0.599240\pi$
$242$	−3.52616	+	4.81620i	−0.226670	+	0.309597i
$243$		0			0
$244$	−16.8715	+	5.48187i	−1.08008	+	0.350941i
$245$	14.6143	+	15.1336i	0.933675	+	0.966848i
$246$		0			0
$247$	0.0864135	−	0.110604i	0.00549836	−	0.00703758i
$248$	−1.51165	−	3.74146i	−0.0959897	−	0.237583i
$249$		0			0
$250$	−1.55147	+	5.41061i	−0.0981234	+	0.342197i
$251$	−1.82747	+	8.59758i	−0.115349	+	0.542675i	0.882085	+	0.471090i	$0.156139\pi$
$251$	−1.82747	+	8.59758i	−0.115349	+	0.542675i	−0.997434	+	0.0715852i	$0.977194\pi$
$252$		0			0
$253$	−27.7871	+	1.40530i	−1.74696	+	0.0883505i
$254$	0.582417	−	0.694097i	0.0365441	−	0.0435515i
$255$		0			0
$256$	−1.18549	+	2.43061i	−0.0740928	+	0.151913i
$257$	14.1871	−	14.6912i	0.884967	−	0.916410i	−0.112042	−	0.993704i	$-0.535739\pi$
$257$	14.1871	−	14.6912i	0.884967	−	0.916410i	0.997008	+	0.0772936i	$0.0246279\pi$
$258$		0			0
$259$	−2.07165	−	3.31534i	−0.128726	−	0.206005i
$260$	14.7332	+	6.55964i	0.913714	+	0.406812i
$261$		0			0
$262$	4.25967	+	0.905420i	0.263163	+	0.0559370i
$263$	6.62272	−	2.41047i	0.408374	−	0.148636i	−0.129661	−	0.991558i	$-0.541389\pi$
$263$	6.62272	−	2.41047i	0.408374	−	0.148636i	0.538035	+	0.842922i	$0.319167\pi$
$264$		0			0
$265$	2.49395	−	2.09267i	0.153202	−	0.128552i
$266$	0.00107756	−	0.0308573i	6.60694e−5	−	0.00189198i
$267$		0			0
$268$	1.82580	+	3.74345i	0.111529	+	0.228667i
$269$	−12.3185	−	4.00253i	−0.751074	−	0.244039i	−0.0916309	−	0.995793i	$-0.529208\pi$
$269$	−12.3185	−	4.00253i	−0.751074	−	0.244039i	−0.659443	+	0.751754i	$0.729208\pi$
$270$		0			0
$271$	16.4548	+	22.6480i	0.999556	+	1.37577i	0.925598	+	0.378509i	$0.123563\pi$
$271$	16.4548	+	22.6480i	0.999556	+	1.37577i	0.0739580	+	0.997261i	$0.476437\pi$
$272$	2.93115	−	2.83058i	0.177727	−	0.171629i
$273$		0			0
$274$	−3.33385	+	9.15968i	−0.201405	+	0.553356i
$275$	−24.0668	−	10.2677i	−1.45128	−	0.619167i
$276$		0			0
$277$	15.6164	−	12.2009i	0.938298	−	0.733079i	−0.0255102	−	0.999675i	$-0.508121\pi$
$277$	15.6164	−	12.2009i	0.938298	−	0.733079i	0.963808	+	0.266596i	$0.0858988\pi$
$278$	−4.53233	−	10.1798i	−0.271831	−	0.610543i
$279$		0			0
$280$	7.53951	−	1.60257i	0.450572	−	0.0957720i
$281$	−3.80981	+	2.38064i	−0.227274	+	0.142017i	−0.638777	−	0.769392i	$-0.720560\pi$
$281$	−3.80981	+	2.38064i	−0.227274	+	0.142017i	0.411503	+	0.911408i	$0.365004\pi$
$282$		0			0
$283$	−0.447851	−	0.218432i	−0.0266220	−	0.0129844i	0.425012	−	0.905188i	$-0.360270\pi$
$283$	−0.447851	−	0.218432i	−0.0266220	−	0.0129844i	−0.451634	+	0.892203i	$0.649159\pi$
$284$	2.01906	+	3.79730i	0.119809	+	0.225328i
$285$		0			0
$286$	2.44883	−	4.05871i	0.144803	−	0.239996i
$287$	−10.0493	+	5.80197i	−0.593192	+	0.342480i
$288$		0			0
$289$	−12.7120	+	5.65976i	−0.747766	+	0.332927i
$290$	14.2222	+	9.59297i	0.835154	+	0.563319i
$291$		0			0
$292$	14.4701	−	5.84631i	0.846799	−	0.342129i
$293$	−31.5713	+	9.05293i	−1.84442	+	0.528878i	−0.999977	−	0.00677345i	$-0.997844\pi$
$293$	−31.5713	+	9.05293i	−1.84442	+	0.528878i	−0.844439	+	0.535651i	$0.820066\pi$
$294$		0			0
$295$	−28.1615	+	3.95785i	−1.63963	+	0.230435i
$296$	7.36225			0.427922
$297$		0			0
$298$	0.997152			0.0577634
$299$	21.8799	−	3.07503i	1.26535	−	0.177833i
$300$		0			0
$301$	9.63973	−	2.76415i	0.555625	−	0.159323i
$302$	−2.93862	+	1.18728i	−0.169099	+	0.0683204i
$303$		0			0
$304$	−0.102495	−	0.0691335i	−0.00587847	−	0.00396508i
$305$	−34.1136	+	15.1883i	−1.95334	+	0.869682i
$306$		0			0
$307$	−14.1577	+	8.17396i	−0.808023	+	0.466512i	−0.846269	−	0.532756i	$-0.821156\pi$
$307$	−14.1577	+	8.17396i	−0.808023	+	0.466512i	0.0382458	+	0.999268i	$0.487823\pi$
$308$	0.515393	+	6.01773i	0.0293673	+	0.342892i
$309$		0			0
$310$	−1.83546	−	3.45201i	−0.104247	−	0.196061i
$311$	3.21980	+	1.57040i	0.182578	+	0.0890494i	0.527393	−	0.849621i	$-0.323169\pi$
$311$	3.21980	+	1.57040i	0.182578	+	0.0890494i	−0.344815	+	0.938671i	$0.612058\pi$
$312$		0			0
$313$	10.1456	−	6.33968i	0.573464	−	0.358340i	−0.211979	−	0.977274i	$-0.567991\pi$
$313$	10.1456	−	6.33968i	0.573464	−	0.358340i	0.785443	+	0.618934i	$0.212435\pi$
$314$	−8.65380	+	1.83942i	−0.488362	+	0.103805i
$315$		0			0
$316$	1.54506	+	3.47025i	0.0869162	+	0.195217i
$317$	19.5234	−	15.2534i	1.09654	−	0.856714i	0.106062	−	0.994360i	$-0.466176\pi$
$317$	19.5234	−	15.2534i	1.09654	−	0.856714i	0.990482	+	0.137646i	$0.0439535\pi$
$318$		0			0
$319$	−19.2007	+	22.0064i	−1.07503	+	1.23212i
$320$	2.17892	−	5.98655i	0.121806	−	0.334658i
$321$		0			0
$322$	3.49631	−	3.37635i	0.194842	−	0.188156i
$323$	−0.0550163	−	0.0757235i	−0.00306119	−	0.00421337i
$324$		0			0
$325$	19.7620	+	6.42107i	1.09620	+	0.356177i
$326$	−1.98610	−	4.07211i	−0.110000	−	0.225533i
$327$		0			0
$328$	0.762655	−	21.8396i	0.0421106	−	1.20589i
$329$	0.470432	−	0.394739i	0.0259358	−	0.0217627i
$330$		0			0
$331$	−19.3560	+	7.04503i	−1.06390	+	0.387230i	−0.813894	−	0.581013i	$-0.802656\pi$
$331$	−19.3560	+	7.04503i	−1.06390	+	0.387230i	−0.250011	+	0.968243i	$0.580434\pi$
$332$	16.3733	+	3.48026i	0.898603	+	0.191004i
$333$		0			0
$334$	−1.97926	−	0.881224i	−0.108300	−	0.0482184i
$335$	4.64593	+	7.43504i	0.253834	+	0.406219i
$336$		0			0
$337$	−9.36026	+	9.69284i	−0.509886	+	0.528002i	−0.924087	−	0.382183i	$-0.875172\pi$
$337$	−9.36026	+	9.69284i	−0.509886	+	0.528002i	0.414201	+	0.910186i	$0.364061\pi$
$338$	1.44221	−	2.95698i	0.0784460	−	0.160838i
$339$		0			0
$340$	6.91302	−	8.23861i	0.374911	−	0.446801i
$341$	6.21818	−	2.37389i	0.336733	−	0.128554i
$342$		0			0
$343$	2.85482	−	13.4309i	0.154146	−	0.725200i
$344$	−5.20552	+	18.1538i	−0.280663	+	0.978789i
$345$		0			0
$346$	−3.52945	−	8.73571i	−0.189745	−	0.469635i
$347$	−12.5855	+	16.1087i	−0.675624	+	0.864759i	−0.996605	−	0.0823263i	$-0.973765\pi$
$347$	−12.5855	+	16.1087i	−0.675624	+	0.864759i	0.320982	+	0.947085i	$0.395987\pi$
$348$		0			0
$349$	−20.1038	−	20.8181i	−1.07613	−	1.11437i	−0.993034	−	0.117824i	$-0.962408\pi$
$349$	−20.1038	−	20.8181i	−1.07613	−	1.11437i	−0.0830962	−	0.996542i	$-0.526481\pi$
$350$	4.34724	−	1.41250i	0.232370	−	0.0755015i
$351$		0			0
$352$	−15.5899	−	7.97940i	−0.830944	−	0.425303i
$353$	−27.2570	−	4.80614i	−1.45074	−	0.255805i	−0.607921	−	0.793997i	$-0.707996\pi$
$353$	−27.2570	−	4.80614i	−1.45074	−	0.255805i	−0.842822	+	0.538192i	$0.819107\pi$
$354$		0			0
$355$	5.06236	+	7.50526i	0.268682	+	0.398338i
$356$	−16.5192	−	4.11869i	−0.875514	−	0.218290i
$357$		0			0
$358$	6.56774	−	0.229351i	0.347116	−	0.0121216i
$359$	−1.65504	−	15.7466i	−0.0873495	−	0.831075i	−0.947225	−	0.320570i	$-0.896125\pi$
$359$	−1.65504	−	15.7466i	−0.0873495	−	0.831075i	0.859875	−	0.510504i	$-0.170541\pi$
$360$		0			0
$361$	12.7116	−	14.1176i	0.669031	−	0.743034i
$362$	−2.43135	−	2.04014i	−0.127789	−	0.107228i
$363$		0			0
$364$	−0.832885	−	4.72352i	−0.0436550	−	0.247580i
$365$	29.0063	−	15.4229i	1.51826	−	0.807272i
$366$		0			0
$367$	19.7769	+	1.38293i	1.03234	+	0.0721886i	0.575865	−	0.817545i	$-0.304666\pi$
$367$	19.7769	+	1.38293i	1.03234	+	0.0721886i	0.456480	+	0.889734i	$0.349110\pi$
$368$	−4.04631	−	19.0364i	−0.210929	−	0.992341i
$369$		0			0
$370$	7.09392	−	0.745601i	0.368795	−	0.0387620i
$371$	−0.930729	−	0.266882i	−0.0483210	−	0.0138558i
$372$		0			0
$373$	7.88362	+	9.39534i	0.408199	+	0.486472i	0.930502	−	0.366288i	$-0.119371\pi$
$373$	7.88362	+	9.39534i	0.408199	+	0.486472i	−0.522303	+	0.852760i	$0.674927\pi$
$374$	−2.15161	−	2.31580i	−0.111257	−	0.119747i
$375$		0			0
$376$	0.160954	+	1.14525i	0.00830056	+	0.0590615i
$377$	13.6325	−	18.7635i	0.702110	−	0.966371i
$378$		0			0
$379$	−3.89229	+	11.9792i	−0.199934	+	0.615332i	0.799950	+	0.600067i	$0.204859\pi$
$379$	−3.89229	+	11.9792i	−0.199934	+	0.615332i	−0.999883	+	0.0152656i	$0.995141\pi$
$380$	−0.288110	−	0.153191i	−0.0147797	−	0.00785852i
$381$		0			0
$382$	2.30123	−	1.55220i	0.117741	−	0.0794173i
$383$	3.26429	−	5.22395i	0.166797	−	0.266932i	−0.754081	−	0.656781i	$-0.771917\pi$
$383$	3.26429	−	5.22395i	0.166797	−	0.266932i	0.920879	+	0.389850i	$0.127473\pi$
$384$		0			0
$385$	2.40305	+	12.4845i	0.122471	+	0.636269i
$386$	9.02595	+	5.21114i	0.459409	+	0.265240i
$387$		0			0
$388$	1.15758	−	11.0137i	0.0587674	−	0.559135i
$389$	1.62287	−	23.2081i	0.0822828	−	1.17670i	−0.764451	−	0.644682i	$-0.776990\pi$
$389$	1.62287	−	23.2081i	0.0822828	−	1.17670i	0.846734	−	0.532017i	$-0.178566\pi$
$390$		0			0
$391$	2.05061	−	14.5908i	0.103704	−	0.737889i
$392$	8.47603	+	8.18521i	0.428104	+	0.413416i
$393$		0			0
$394$	2.10942	−	5.22099i	0.106271	−	0.263029i
$395$	3.99809	+	6.92489i	0.201166	+	0.348429i
$396$		0			0
$397$	7.41242	−	12.8387i	0.372018	−	0.644355i	−0.617857	−	0.786290i	$-0.711999\pi$
$397$	7.41242	−	12.8387i	0.372018	−	0.644355i	0.989876	+	0.141935i	$0.0453325\pi$
$398$	−8.81735	−	11.2857i	−0.441974	−	0.565701i
$399$		0			0
$400$	4.42779	−	17.7589i	0.221390	−	0.887945i
$401$	9.14444	+	7.14442i	0.456652	+	0.356775i	0.817577	−	0.575819i	$-0.195317\pi$
$401$	9.14444	+	7.14442i	0.456652	+	0.356775i	−0.360925	+	0.932595i	$0.617539\pi$
$402$		0			0
$403$	−4.75075	+	2.31710i	−0.236652	+	0.115423i
$404$	−1.64647	−	1.19623i	−0.0819151	−	0.0595148i
$405$		0			0
$406$		−	5.10199i		−	0.253207i
$407$	−0.234141	+	12.1412i	−0.0116059	+	0.601817i
$408$		0			0
$409$	15.0665	+	0.526134i	0.744991	+	0.0260156i	0.404880	−	0.914370i	$-0.367313\pi$
$409$	15.0665	+	0.526134i	0.744991	+	0.0260156i	0.340111	+	0.940385i	$0.389536\pi$
$410$	−1.47691	−	21.1208i	−0.0729395	−	1.04308i
$411$		0			0
$412$	0.425011	+	12.1707i	0.0209388	+	0.599608i
$413$	5.65930	+	6.28528i	0.278476	+	0.309279i
$414$		0			0
$415$	35.0427	+	3.68314i	1.72018	+	0.180798i
$416$	12.8952	+	5.21001i	0.632240	+	0.255442i
$417$		0			0
$418$	−0.0551545	+	0.0784629i	−0.00269769	+	0.00383775i
$419$	−29.6409	+	5.22648i	−1.44805	+	0.255330i	−0.841734	−	0.539892i	$-0.818465\pi$
$419$	−29.6409	+	5.22648i	−1.44805	+	0.255330i	−0.606317	+	0.795223i	$0.707354\pi$
$420$		0			0
$421$	−2.27311	−	9.11694i	−0.110785	−	0.444332i	0.889127	−	0.457661i	$-0.151313\pi$
$421$	−2.27311	−	9.11694i	−0.110785	−	0.444332i	−0.999911	+	0.0133288i	$0.995757\pi$
$422$	0.0830269	−	0.186481i	0.00404168	−	0.00907777i
$423$		0			0
$424$	1.35506	−	1.22010i	0.0658075	−	0.0592533i
$425$	7.74854	−	11.4877i	0.375859	−	0.557235i
$426$		0			0
$427$	9.41815	+	5.88512i	0.455776	+	0.284801i
$428$	25.5297	+	9.29204i	1.23402	+	0.449148i
$429$		0			0
$430$	−3.17730	+	18.0194i	−0.153223	+	0.868971i
$431$	−1.95441	−	6.01505i	−0.0941406	−	0.289735i	0.892888	−	0.450278i	$-0.148675\pi$
$431$	−1.95441	−	6.01505i	−0.0941406	−	0.289735i	−0.987029	+	0.160544i	$0.948675\pi$
$432$		0			0
$433$	−2.99784	+	2.17806i	−0.144067	+	0.104671i	−0.657484	−	0.753468i	$-0.728379\pi$
$433$	−2.99784	+	2.17806i	−0.144067	+	0.104671i	0.513417	+	0.858139i	$0.328379\pi$
$434$	−0.545876	+	1.02664i	−0.0262029	+	0.0492805i
$435$		0			0
$436$	8.91173	+	31.0789i	0.426795	+	1.48841i
$437$	−0.445955	+	0.0311842i	−0.0213329	+	0.00149174i
$438$		0			0
$439$	1.51479	+	4.16186i	0.0722971	+	0.198635i	0.970578	−	0.240787i	$-0.0774056\pi$
$439$	1.51479	+	4.16186i	0.0722971	+	0.198635i	−0.898281	+	0.439422i	$0.855183\pi$
$440$	−22.3367	−	8.62118i	−1.06486	−	0.410999i
$441$		0			0
$442$	1.86553	+	1.67973i	0.0887343	+	0.0798967i
$443$	26.2850	−	6.55359i	1.24884	−	0.311370i	0.439248	−	0.898366i	$-0.355245\pi$
$443$	26.2850	−	6.55359i	1.24884	−	0.311370i	0.809590	+	0.586995i	$0.199689\pi$
$444$		0			0
$445$	−35.4885	−	4.98759i	−1.68232	−	0.236434i
$446$	0.0238362	+	0.00334995i	0.00112868	+	0.000158625i
$447$		0			0
$448$	−1.83841	+	0.458367i	−0.0868568	+	0.0216558i
$449$	−29.3966	−	26.4688i	−1.38731	−	1.24914i	−0.933755	−	0.357912i	$-0.883489\pi$
$449$	−29.3966	−	26.4688i	−1.38731	−	1.24914i	−0.453555	−	0.891228i	$-0.649845\pi$
$450$		0			0
$451$	35.9917	+	1.95227i	1.69478	+	0.0919287i
$452$	−2.75104	−	7.55841i	−0.129398	−	0.355518i
$453$		0			0
$454$	4.57989	−	0.320257i	0.214945	−	0.0150304i
$455$	−2.78294	−	9.70526i	−0.130466	−	0.454990i
$456$		0			0
$457$	−5.56440	+	10.4651i	−0.260292	+	0.489537i	−0.978488	−	0.206303i	$-0.933857\pi$
$457$	−5.56440	+	10.4651i	−0.260292	+	0.489537i	0.718197	+	0.695840i	$0.244968\pi$
$458$	3.98195	−	2.89306i	0.186064	−	0.135184i
$459$		0			0
$460$	−15.8730	−	48.8521i	−0.740083	−	2.27774i
$461$	−0.142306	+	0.807056i	−0.00662784	+	0.0375883i	−0.987942	−	0.154822i	$-0.950519\pi$
$461$	−0.142306	+	0.807056i	−0.00662784	+	0.0375883i	0.981314	+	0.192411i	$0.0616306\pi$
$462$		0			0
$463$	0.626971	+	0.228199i	0.0291378	+	0.0106053i	0.356548	−	0.934277i	$-0.383954\pi$
$463$	0.626971	+	0.228199i	0.0291378	+	0.0106053i	−0.327410	+	0.944882i	$0.606176\pi$
$464$	−17.3247	−	10.8256i	−0.804277	−	0.502568i
$465$		0			0
$466$	−3.55525	+	5.27087i	−0.164694	+	0.244168i
$467$	14.9874	−	13.4947i	0.693535	−	0.624461i	−0.245050	−	0.969510i	$-0.578804\pi$
$467$	14.9874	−	13.4947i	0.693535	−	0.624461i	0.938585	+	0.345049i	$0.112138\pi$
$468$		0			0
$469$	1.06053	−	2.38199i	0.0489708	−	0.109990i
$470$	0.271071	+	1.08721i	0.0125036	+	0.0501491i
$471$		0			0
$472$	−15.6858	+	2.76583i	−0.721997	+	0.127307i
$473$	−29.7722	−	9.16186i	−1.36893	−	0.421263i
$474$		0			0
$475$	−0.389805	−	0.157491i	−0.0178855	−	0.00722620i
$476$	−3.18099	−	0.334336i	−0.145800	−	0.0153242i
$477$		0			0
$478$	6.11586	+	6.79235i	0.279733	+	0.310675i
$479$	0.287530	+	8.23378i	0.0131376	+	0.376211i	0.988097	+	0.153830i	$0.0491608\pi$
$479$	0.287530	+	8.23378i	0.0131376	+	0.376211i	−0.974960	+	0.222381i	$0.928617\pi$
$480$		0			0
$481$	−0.672701	−	9.62007i	−0.0306725	−	0.438638i
$482$	−2.30358	−	0.0804427i	−0.104925	−	0.00366407i
$483$		0			0
$484$	8.86827	−	16.5326i	0.403103	−	0.751482i
$485$		−	23.3114i		−	1.05852i
$486$		0			0
$487$	28.2137	+	20.4984i	1.27848	+	0.928873i	0.999506	−	0.0314241i	$-0.0100043\pi$
$487$	28.2137	+	20.4984i	1.27848	+	0.928873i	0.278978	+	0.960297i	$0.410004\pi$
$488$	−18.7979	+	9.16833i	−0.850940	+	0.415031i
$489$		0			0
$490$	8.99606	+	7.02849i	0.406400	+	0.317515i
$491$	−1.16625	+	4.67757i	−0.0526321	+	0.211096i	−0.990854	−	0.134938i	$-0.956916\pi$
$491$	−1.16625	+	4.67757i	−0.0526321	+	0.211096i	0.938222	+	0.346034i	$0.112472\pi$
$492$		0			0
$493$	−9.52209	−	12.1877i	−0.428854	−	0.548907i
$494$	0.0380822	−	0.0659603i	0.00171340	−	0.00296770i
$495$		0			0
$496$	2.32787	+	4.03199i	0.104525	+	0.181042i
$497$	1.00859	−	2.49635i	0.0452415	−	0.111977i
$498$		0			0
$499$	13.9416	+	13.4632i	0.624111	+	0.602697i	0.937946	−	0.346780i	$-0.112725\pi$
$499$	13.9416	+	13.4632i	0.624111	+	0.602697i	−0.313835	+	0.949477i	$0.601614\pi$
$500$	2.46212	−	17.5189i	0.110109	−	0.783469i
$501$		0			0
$502$	−0.332713	+	4.75801i	−0.0148497	+	0.212361i
$503$	1.94852	−	18.5389i	0.0868802	−	0.826610i	−0.861133	−	0.508380i	$-0.830245\pi$
$503$	1.94852	−	18.5389i	0.0868802	−	0.826610i	0.948013	−	0.318231i	$-0.103089\pi$
$504$		0			0
$505$	−3.71004	−	2.14199i	−0.165095	−	0.0953174i
$506$	−14.8256	+	2.85367i	−0.659077	+	0.126861i
$507$		0			0
$508$	−1.50913	+	2.41511i	−0.0669566	+	0.107153i
$509$	−6.79118	+	4.58071i	−0.301014	+	0.203036i	−0.700408	−	0.713743i	$-0.746998\pi$
$509$	−6.79118	+	4.58071i	−0.301014	+	0.203036i	0.399394	+	0.916779i	$0.369221\pi$
$510$		0			0
$511$	−8.62661	−	4.58685i	−0.381619	−	0.202910i
$512$	6.66865	−	20.5240i	0.294716	−	0.907041i
$513$		0			0
$514$	6.51409	−	8.96587i	0.287324	−	0.395468i
$515$	3.56769	+	25.3854i	0.157211	+	1.11862i
$516$		0			0
$517$	−1.89376	+	0.229009i	−0.0832876	+	0.0100718i
$518$	−1.36360	−	1.62508i	−0.0599132	−	0.0714018i
$519$		0			0
$520$	18.2772	+	5.24091i	0.801510	+	0.229829i
$521$	−22.9892	+	2.41626i	−1.00717	+	0.105858i	−0.593724	−	0.804669i	$-0.702343\pi$
$521$	−22.9892	+	2.41626i	−1.00717	+	0.105858i	−0.413450	+	0.910527i	$0.635676\pi$
$522$		0			0
$523$	−5.19998	−	24.4640i	−0.227379	−	1.06973i	−0.932646	−	0.360793i	$-0.882506\pi$
$523$	−5.19998	−	24.4640i	−0.227379	−	1.06973i	0.705267	−	0.708942i	$-0.250827\pi$
$524$	−13.6540	−	0.954784i	−0.596480	−	0.0417099i
$525$		0			0
$526$	3.37674	−	1.79545i	0.147233	−	0.0782852i
$527$	0.612077	+	3.47126i	0.0266625	+	0.151210i
$528$		0			0
$529$	−36.2895	−	30.4505i	−1.57781	−	1.32394i
$530$	1.18211	−	1.31286i	0.0513475	−	0.0570272i
$531$		0			0
$532$	0.0101439	+	0.0965130i	0.000439795	+	0.00418437i
$533$	−28.6069	+	0.998976i	−1.23910	+	0.0432705i
$534$		0			0
$535$	55.4900	+	13.8352i	2.39904	+	0.598148i
$536$	2.74584	+	4.07088i	0.118602	+	0.175835i
$537$		0			0
$538$	−6.92177	−	1.22049i	−0.298419	−	0.0526192i
$539$	−13.7679	+	13.7177i	−0.593027	+	0.590861i
$540$		0			0
$541$	−8.47526	+	2.75378i	−0.364380	+	0.118394i	−0.485484	−	0.874246i	$-0.661357\pi$
$541$	−8.47526	+	2.75378i	−0.364380	+	0.118394i	0.121104	+	0.992640i	$0.461357\pi$
$542$	10.5525	+	10.9275i	0.453270	+	0.469375i
$543$		0			0
$544$	5.71003	−	7.30851i	0.244816	−	0.313350i
$545$	25.4947	+	63.1017i	1.09207	+	2.70298i
$546$		0			0
$547$	−10.3311	+	36.0290i	−0.441728	+	1.54049i	0.354243	+	0.935153i	$0.384739\pi$
$547$	−10.3311	+	36.0290i	−0.441728	+	1.54049i	−0.795971	+	0.605335i	$0.793039\pi$
$548$	6.36975	−	29.9673i	0.272102	−	1.28014i
$549$		0			0
$550$	−13.7080	−	3.69992i	−0.584509	−	0.157765i
$551$	−0.301635	+	0.359474i	−0.0128501	+	0.0153141i
$552$		0			0
$553$	1.04249	−	2.13742i	0.0443312	−	0.0908925i
$554$	7.47021	−	7.73563i	0.317379	−	0.328655i
$555$		0			0
$556$	18.5596	+	29.7015i	0.787101	+	1.25962i
$557$	29.4829	+	13.1266i	1.24923	+	0.556193i	0.921426	−	0.388553i	$-0.127025\pi$
$557$	29.4829	+	13.1266i	1.24923	+	0.556193i	0.327803	+	0.944746i	$0.393692\pi$
$558$		0			0
$559$	24.1968	+	5.14319i	1.02342	+	0.217534i
$560$	−8.35677	+	3.04162i	−0.353138	+	0.128532i
$561$		0			0
$562$	−1.86745	+	1.56698i	−0.0787738	+	0.0660990i
$563$	−1.08873	+	31.1771i	−0.0458844	+	1.31396i	0.730158	+	0.683278i	$0.239446\pi$
$563$	−1.08873	+	31.1771i	−0.0458844	+	1.31396i	−0.776043	+	0.630680i	$0.782776\pi$
$564$		0			0
$565$	−7.42229	−	15.2180i	−0.312258	−	0.640224i
$566$	−0.257154	−	0.0835543i	−0.0108090	−	0.00351205i
$567$		0			0
$568$	2.98031	+	4.10204i	0.125051	+	0.172118i
$569$	−11.1522	+	10.7695i	−0.467523	+	0.451481i	−0.890717	−	0.454557i	$-0.849797\pi$
$569$	−11.1522	+	10.7695i	−0.467523	+	0.451481i	0.423195	+	0.906039i	$0.360909\pi$
$570$		0			0
$571$	0.309692	−	0.850873i	0.0129602	−	0.0356079i	−0.933044	−	0.359763i	$-0.882858\pi$
$571$	0.309692	−	0.850873i	0.0129602	−	0.0356079i	0.946004	+	0.324155i	$0.105080\pi$
$572$	−5.84648	+	13.7037i	−0.244454	+	0.572981i
$573$		0			0
$574$	−4.96193	+	3.87668i	−0.207107	+	0.161810i
$575$	−26.9184	−	60.4596i	−1.12257	−	2.52134i
$576$		0			0
$577$	27.6834	−	5.88428i	1.15247	−	0.244966i	0.408233	−	0.912878i	$-0.366145\pi$
$577$	27.6834	−	5.88428i	1.15247	−	0.244966i	0.744241	+	0.667912i	$0.232812\pi$
$578$	−6.40350	+	4.00135i	−0.266351	+	0.166434i
$579$		0			0
$580$	−48.4620	−	23.6365i	−2.01227	−	0.981451i
$581$	−4.91973	−	9.25266i	−0.204105	−	0.383865i
$582$		0			0
$583$	1.96899	+	2.27345i	0.0815474	+	0.0941568i
$584$	15.9345	−	9.19980i	0.659375	−	0.380690i
$585$		0			0
$586$	−16.2815	+	7.24898i	−0.672582	+	0.299453i
$587$	8.44651	+	5.69724i	0.348625	+	0.235150i	0.721005	−	0.692930i	$-0.243680\pi$
$587$	8.44651	+	5.69724i	0.348625	+	0.235150i	−0.372380	+	0.928080i	$0.621458\pi$
$588$		0			0
$589$	0.0991573	−	0.0400622i	0.00408571	−	0.00165073i
$590$	−14.8340	+	4.25358i	−0.610706	+	0.175117i
$591$		0			0
$592$	−8.41158	+	1.18217i	−0.345714	+	0.0485869i
$593$	35.2916			1.44925			0.724626	−	0.689142i	$-0.242012\pi$
$593$	35.2916			1.44925			0.724626	+	0.689142i	$0.242012\pi$
$594$		0			0
$595$	−6.73285			−0.276020
$596$	−3.10358	+	0.436180i	−0.127128	+	0.0178666i
$597$		0			0
$598$	11.5252	−	3.30479i	0.471300	−	0.135143i
$599$	12.7896	−	5.16735i	0.522570	−	0.211132i	−0.0981392	−	0.995173i	$-0.531289\pi$
$599$	12.7896	−	5.16735i	0.522570	−	0.211132i	0.620710	+	0.784041i	$0.286845\pi$
$600$		0			0
$601$	−3.61563	−	2.43878i	−0.147485	−	0.0994797i	0.483234	−	0.875491i	$-0.339462\pi$
$601$	−3.61563	−	2.43878i	−0.147485	−	0.0994797i	−0.630719	+	0.776012i	$0.717240\pi$
$602$	4.97126	−	2.21335i	0.202613	−	0.0902092i
$603$		0			0
$604$	8.62697	−	4.98078i	0.351026	−	0.202665i
$605$	14.9277	−	36.5617i	0.606897	−	1.48644i
$606$		0			0
$607$	15.3953	+	28.9544i	0.624876	+	1.17522i	0.971460	+	0.237203i	$0.0762306\pi$
$607$	15.3953	+	28.9544i	0.624876	+	1.17522i	−0.346584	+	0.938019i	$0.612658\pi$
$608$	−0.252918	−	0.123356i	−0.0102572	−	0.00500276i
$609$		0			0
$610$	−17.1842	+	10.7379i	−0.695770	+	0.434765i
$611$	1.48176	−	0.314958i	0.0599455	−	0.0127418i
$612$		0			0
$613$	−3.61714	−	8.12423i	−0.146095	−	0.328134i	0.825645	−	0.564191i	$-0.190812\pi$
$613$	−3.61714	−	8.12423i	−0.146095	−	0.328134i	−0.971739	+	0.236056i	$0.924145\pi$
$614$	−6.99048	+	5.46156i	−0.282113	+	0.220411i
$615$		0			0
$616$	1.58911	+	6.94110i	0.0640272	+	0.279665i
$617$	4.75525	−	13.0649i	0.191439	−	0.525975i	−0.806422	−	0.591340i	$-0.798599\pi$
$617$	4.75525	−	13.0649i	0.191439	−	0.525975i	0.997861	+	0.0653652i	$0.0208212\pi$
$618$		0			0
$619$	−28.8044	+	27.8161i	−1.15775	+	1.11802i	−0.166495	+	0.986042i	$0.553245\pi$
$619$	−28.8044	+	27.8161i	−1.15775	+	1.11802i	−0.991252	+	0.131981i	$0.957866\pi$
$620$	7.22278	+	9.94131i	0.290074	+	0.399253i
$621$		0			0
$622$	1.84879	+	0.600709i	0.0741298	+	0.0240862i
$623$	4.67224	+	9.57951i	0.187189	+	0.383795i
$624$		0			0
$625$	−0.0770034	+	2.20509i	−0.00308013	+	0.0882035i
$626$	4.97307	−	4.17290i	0.198764	−	0.166783i
$627$		0			0
$628$	26.1299	−	9.51050i	1.04270	−	0.379510i
$629$	−6.29036	−	1.33706i	−0.250813	−	0.0533120i
$630$		0			0
$631$	−16.2036	−	7.21432i	−0.645056	−	0.287197i	0.0580165	−	0.998316i	$-0.481522\pi$
$631$	−16.2036	−	7.21432i	−0.645056	−	0.287197i	−0.703073	+	0.711118i	$0.748189\pi$
$632$	2.37325	+	3.79799i	0.0944027	+	0.151076i
$633$		0			0
$634$	9.33915	−	9.67097i	0.370905	−	0.384083i
$635$	−2.62790	+	5.38799i	−0.104285	+	0.213816i
$636$		0			0
$637$	9.92095	−	11.8233i	0.393082	−	0.468457i
$638$	−8.65574	+	13.2754i	−0.342684	+	0.525580i
$639$		0			0
$640$	8.60180	−	40.4683i	0.340016	−	1.59965i
$641$	9.59436	−	33.4595i	0.378954	−	1.32157i	−0.508653	−	0.860971i	$-0.669857\pi$
$641$	9.59436	−	33.4595i	0.378954	−	1.32157i	0.887608	−	0.460600i	$-0.152366\pi$
$642$		0			0
$643$	−4.40635	−	10.9061i	−0.173769	−	0.430094i	0.815016	−	0.579439i	$-0.196728\pi$
$643$	−4.40635	−	10.9061i	−0.173769	−	0.430094i	−0.988785	+	0.149344i	$0.952284\pi$
$644$	−9.40518	+	12.0381i	−0.370616	+	0.474367i
$645$		0			0
$646$	−0.0352823	−	0.0365359i	−0.00138816	−	0.00143749i
$647$	5.95410	−	1.93461i	0.234080	−	0.0760572i	−0.189628	−	0.981856i	$-0.560728\pi$
$647$	5.95410	−	1.93461i	0.234080	−	0.0760572i	0.423708	+	0.905799i	$0.360728\pi$
$648$		0			0
$649$	−4.06232	−	25.9556i	−0.159460	−	1.01885i
$650$	11.1042	+	1.95798i	0.435544	+	0.0767982i
$651$		0			0
$652$	7.96287	+	11.8054i	0.311850	+	0.462337i
$653$	−4.17707	−	1.04146i	−0.163461	−	0.0407555i	0.159332	−	0.987225i	$-0.449066\pi$
$653$	−4.17707	−	1.04146i	−0.163461	−	0.0407555i	−0.322793	+	0.946470i	$0.604622\pi$
$654$		0			0
$655$	−28.7943	+	1.00552i	−1.12509	+	0.0392889i
$656$	2.63547	+	25.0748i	0.102898	+	0.979006i
$657$		0			0
$658$	0.222980	−	0.247645i	0.00869268	−	0.00965419i
$659$	27.5014	+	23.0764i	1.07130	+	0.898930i	0.995170	−	0.0981673i	$-0.0312980\pi$
$659$	27.5014	+	23.0764i	1.07130	+	0.898930i	0.0761335	+	0.997098i	$0.475742\pi$
$660$		0			0
$661$	0.340867	+	1.93315i	0.0132582	+	0.0751910i	0.990719	−	0.135926i	$-0.0434010\pi$
$661$	0.340867	+	1.93315i	0.0132582	+	0.0751910i	−0.977461	+	0.211117i	$0.932290\pi$
$662$	−9.86912	+	5.24751i	−0.383574	+	0.203950i
$663$		0			0
$664$	19.6868	+	1.37664i	0.763997	+	0.0534239i
$665$	0.0424719	+	0.199814i	0.00164699	+	0.00774847i
$666$		0			0
$667$	−73.4652	+	7.72151i	−2.84459	+	0.298978i
$668$	6.54582	+	1.87698i	0.253265	+	0.0726227i
$669$		0			0
$670$	3.05804	+	3.64443i	0.118142	+	0.140797i
$671$	−14.5218	−	31.2915i	−0.560609	−	1.20799i
$672$		0			0
$673$	−0.0277930	−	0.197758i	−0.00107134	−	0.00762299i	0.989725	−	0.142984i	$-0.0456696\pi$
$673$	−0.0277930	−	0.197758i	−0.00107134	−	0.00762299i	−0.990796	+	0.135361i	$0.956781\pi$
$674$	−4.29782	+	5.91544i	−0.165546	+	0.227854i
$675$		0			0
$676$	−3.19536	+	9.83429i	−0.122898	+	0.378242i
$677$	6.93865	+	3.68935i	0.266674	+	0.141793i	0.597425	−	0.801925i	$-0.296191\pi$
$677$	6.93865	+	3.68935i	0.266674	+	0.141793i	−0.330751	+	0.943718i	$0.607302\pi$
$678$		0			0
$679$	−5.74766	+	3.87685i	−0.220575	+	0.148780i
$680$	6.71911	−	10.7528i	0.257666	−	0.412352i
$681$		0			0
$682$	3.16212	−	1.74524i	0.121084	−	0.0668287i
$683$	34.5551	+	19.9504i	1.32221	+	0.763380i	0.984081	−	0.177719i	$-0.0568719\pi$
$683$	34.5551	+	19.9504i	1.32221	+	0.763380i	0.338131	+	0.941099i	$0.390205\pi$
$684$		0			0
$685$	6.74108	−	64.1371i	0.257563	−	2.45055i
$686$	0.519754	−	7.43283i	0.0198443	−	0.283787i
$687$		0			0
$688$	3.03247	−	21.5771i	0.115612	−	0.822620i
$689$	−1.71809	−	1.65914i	−0.0654540	−	0.0632082i
$690$		0			0
$691$	14.3439	−	35.5025i	0.545669	−	1.35058i	−0.362504	−	0.931982i	$-0.618078\pi$
$691$	14.3439	−	35.5025i	0.545669	−	1.35058i	0.908173	−	0.418596i	$-0.137478\pi$
$692$	14.8065	+	25.6456i	0.562858	+	0.974898i
$693$		0			0
$694$	−5.54639	+	9.60663i	−0.210538	+	0.364663i
$695$	45.3890	+	58.0953i	1.72170	+	2.20368i
$696$		0			0
$697$	−4.61790	+	18.5214i	−0.174915	+	0.701547i
$698$	−12.3752	−	9.66855i	−0.468407	−	0.365960i
$699$		0			0
$700$	−12.9127	+	6.29794i	−0.488054	+	0.238040i
$701$	25.9677	+	18.8666i	0.980787	+	0.712583i	0.957884	−	0.287154i	$-0.0927093\pi$
$701$	25.9677	+	18.8666i	0.980787	+	0.712583i	0.0229024	+	0.999738i	$0.492709\pi$
$702$		0			0
$703$			0.195117i			0.00735896i
$704$	5.56121	+	1.92626i	0.209596	+	0.0725988i
$705$		0			0
$706$	−15.0098	−	0.524153i	−0.564901	−	0.0197268i
$707$	0.0888752	+	1.27097i	0.00334249	+	0.0477999i
$708$		0			0
$709$	0.366215	+	10.4870i	0.0137535	+	0.393849i	0.986674	+	0.162709i	$0.0520232\pi$
$709$	0.366215	+	10.4870i	0.0137535	+	0.393849i	−0.972921	+	0.231140i	$0.925755\pi$
$710$	3.28712	+	3.65071i	0.123363	+	0.137009i
$711$		0			0
$712$	−19.9618	−	2.09807i	−0.748102	−	0.0786286i
$713$	15.6091	+	6.30650i	0.584566	+	0.236180i
$714$		0			0
$715$	−9.22414	+	29.9746i	−0.344963	+	1.12099i
$716$	−20.3414	+	3.58674i	−0.760195	+	0.134043i
$717$		0			0
$718$	−2.07855	−	8.33662i	−0.0775709	−	0.311120i
$719$	−19.9909	+	44.9004i	−0.745536	+	1.67450i	−0.00728560	+	0.999973i	$0.502319\pi$
$719$	−19.9909	+	44.9004i	−0.745536	+	1.67450i	−0.738250	+	0.674527i	$0.764348\pi$
$720$		0			0
$721$	5.66569	−	5.10141i	0.211001	−	0.189987i
$722$	5.76452	−	8.54625i	0.214533	−	0.318059i
$723$		0			0
$724$	8.45986	+	5.28631i	0.314408	+	0.196464i
$725$	−65.2807	−	23.7602i	−2.42446	−	0.882433i
$726$		0			0
$727$	−3.86949	+	21.9450i	−0.143511	+	0.813894i	0.825039	+	0.565076i	$0.191153\pi$
$727$	−3.86949	+	21.9450i	−0.143511	+	0.813894i	−0.968550	+	0.248818i	$0.919958\pi$
$728$	−1.74743	−	5.37803i	−0.0647640	−	0.199323i
$729$		0			0
$730$	14.4221	−	10.4782i	0.533785	−	0.387817i
$731$	7.74455	−	14.5654i	0.286443	−	0.538720i
$732$		0			0
$733$	0.181640	+	0.633455i	0.00670904	+	0.0233972i	0.964545	−	0.263918i	$-0.0850149\pi$
$733$	0.181640	+	0.633455i	0.00670904	+	0.0233972i	−0.957836	+	0.287316i	$0.907237\pi$
$734$	10.7317	−	0.750437i	0.396116	−	0.0276991i
$735$		0			0
$736$	−15.1504	−	41.6255i	−0.558453	−	1.53434i
$737$	−6.80068	+	4.39875i	−0.250506	+	0.162030i
$738$		0			0
$739$	−11.1411	−	10.0315i	−0.409831	−	0.369014i	0.438274	−	0.898841i	$-0.355590\pi$
$739$	−11.1411	−	10.0315i	−0.409831	−	0.369014i	−0.848105	+	0.529828i	$0.822257\pi$
$740$	−21.7533	+	5.42371i	−0.799668	+	0.199380i
$741$		0			0
$742$	−0.520292	−	0.0731223i	−0.0191005	−	0.00268440i
$743$	−5.54396	−	0.779153i	−0.203388	−	0.0285843i	0.0367432	−	0.999325i	$-0.488302\pi$
$743$	−5.54396	−	0.779153i	−0.203388	−	0.0285843i	−0.240131	+	0.970740i	$0.577191\pi$
$744$		0			0
$745$	−6.40126	+	1.59601i	−0.234524	+	0.0584734i
$746$	4.94589	+	4.45330i	0.181082	+	0.163047i
$747$		0			0
$748$	7.70977	+	6.26663i	0.281897	+	0.229131i
$749$	−5.81715	−	15.9825i	−0.212554	−	0.583987i
$750$		0			0
$751$	−12.6875	+	0.887193i	−0.462972	+	0.0323741i	−0.299338	−	0.954147i	$-0.596766\pi$
$751$	−12.6875	+	0.887193i	−0.462972	+	0.0323741i	−0.163634	+	0.986521i	$0.552321\pi$
$752$	−0.367789	−	1.28263i	−0.0134119	−	0.0467728i
$753$		0			0
$754$	5.90852	−	11.1123i	0.215176	−	0.404687i
$755$	16.9643	−	12.3253i	0.617395	−	0.448563i
$756$		0			0
$757$	−8.93499	−	27.4991i	−0.324748	−	0.999471i	−0.971554	−	0.236817i	$-0.923896\pi$
$757$	−8.93499	−	27.4991i	−0.324748	−	0.999471i	0.646807	−	0.762654i	$-0.276104\pi$
$758$	−1.18688	+	6.73112i	−0.0431094	+	0.244485i
$759$		0			0
$760$	−0.361503	−	0.131576i	−0.0131131	−	0.00477277i
$761$	18.3085	+	11.4404i	0.663683	+	0.414715i	0.819507	−	0.573070i	$-0.194248\pi$
$761$	18.3085	+	11.4404i	0.663683	+	0.414715i	−0.155823	+	0.987785i	$0.549803\pi$
$762$		0			0
$763$	11.3184	−	16.7802i	0.409753	−	0.607484i
$764$	−6.48348	+	5.83775i	−0.234564	+	0.211202i
$765$		0			0
$766$	1.35958	−	3.05367i	0.0491236	−	0.110334i
$767$	5.04728	+	20.2435i	0.182247	+	0.730951i
$768$		0			0
$769$	46.2586	−	8.15665i	1.66813	−	0.294136i	0.741735	−	0.670693i	$-0.234003\pi$
$769$	46.2586	−	8.15665i	1.66813	−	0.294136i	0.926394	+	0.376556i	$0.122892\pi$
$770$	2.23414	+	6.52719i	0.0805130	+	0.235224i
$771$		0			0
$772$	−30.3723	−	12.2712i	−1.09312	−	0.441650i
$773$	−36.8952	−	3.87784i	−1.32703	−	0.139476i	−0.585650	−	0.810564i	$-0.699161\pi$
$773$	−36.8952	−	3.87784i	−1.32703	−	0.139476i	−0.741378	+	0.671088i	$0.765827\pi$
$774$		0			0
$775$	10.5939	+	11.7657i	0.380543	+	0.422636i
$776$	−0.455658	−	13.0483i	−0.0163572	−	0.468408i
$777$		0			0
$778$	−0.880636	−	12.5937i	−0.0315723	−	0.451505i
$779$	0.578799	+	0.0202121i	0.0207376	+	0.000724174i
$780$		0			0
$781$	−6.85953	+	4.78442i	−0.245453	+	0.171200i
$782$		−	7.99539i		−	0.285914i
$783$		0			0
$784$	−10.9984	−	7.99082i	−0.392801	−	0.285387i
$785$	52.6093	−	25.6593i	1.87771	−	0.915819i
$786$		0			0
$787$	24.3065	+	18.9903i	0.866433	+	0.676932i	0.947493	−	0.319778i	$-0.103608\pi$
$787$	24.3065	+	18.9903i	0.866433	+	0.676932i	−0.0810597	+	0.996709i	$0.525830\pi$
$788$	−4.28165	+	17.1728i	−0.152527	+	0.611754i
$789$		0			0
$790$	2.67139	+	3.41922i	0.0950437	+	0.121650i
$791$	−2.51776	+	4.36088i	−0.0895212	+	0.155055i
$792$		0			0
$793$	13.6976	+	23.7250i	0.486417	+	0.842499i
$794$	3.01355	−	7.45879i	0.106947	−	0.264703i
$795$		0			0
$796$	32.3802	+	31.2692i	1.14769	+	1.10831i
$797$	−2.74561	+	19.5360i	−0.0972545	+	0.692001i	0.879227	+	0.476402i	$0.158059\pi$
$797$	−2.74561	+	19.5360i	−0.0972545	+	0.692001i	−0.976482	+	0.215599i	$0.930830\pi$
$798$		0			0
$799$	0.0704679	−	1.00774i	0.00249297	−	0.0356512i
$800$	4.35451	−	41.4304i	0.153955	−	1.46479i
$801$		0			0
$802$	5.45341	+	3.14853i	0.192567	+	0.111178i
$803$	14.6648	+	26.5705i	0.517509	+	0.937651i
$804$		0			0
$805$	−17.0406	+	27.2707i	−0.600604	+	0.961167i
$806$	−2.37788	+	1.60390i	−0.0837571	+	0.0564949i
$807$		0			0
$808$	−2.11853	−	1.12644i	−0.0745295	−	0.0396280i
$809$	9.46432	−	29.1282i	0.332748	−	1.02409i	−0.635073	−	0.772452i	$-0.719030\pi$
$809$	9.46432	−	29.1282i	0.332748	−	1.02409i	0.967821	−	0.251641i	$-0.0809701\pi$
$810$		0			0
$811$	−23.3881	+	32.1910i	−0.821269	+	1.13038i	0.168217	+	0.985750i	$0.446199\pi$
$811$	−23.3881	+	32.1910i	−0.821269	+	1.13038i	−0.989486	+	0.144630i	$0.953801\pi$
$812$	2.23174	+	15.8797i	0.0783188	+	0.557267i
$813$		0			0
$814$	0.791099	+	6.54188i	0.0277280	+	0.229293i
$815$	19.2676	+	22.9622i	0.674913	+	0.804330i
$816$		0			0
$817$	−0.481118	−	0.137958i	−0.0168322	−	0.00482656i
$818$	8.13587	−	0.855115i	0.284464	−	0.0298984i
$819$		0			0
$820$	13.8356	+	65.0915i	0.483161	+	2.27309i
$821$	−48.1453	−	3.36665i	−1.68028	−	0.117497i	−0.802530	−	0.596611i	$-0.796513\pi$
$821$	−48.1453	−	3.36665i	−1.68028	−	0.117497i	−0.877753	+	0.479114i	$0.840958\pi$
$822$		0			0
$823$	−30.7527	+	16.3515i	−1.07197	+	0.569977i	−0.909061	−	0.416664i	$-0.863199\pi$
$823$	−30.7527	+	16.3515i	−1.07197	+	0.569977i	−0.162911	+	0.986641i	$0.552088\pi$
$824$	2.49318	+	14.1395i	0.0868539	+	0.492573i
$825$		0			0
$826$	3.51575	+	2.95007i	0.122329	+	0.102646i
$827$	3.74060	−	4.15436i	0.130074	−	0.144461i	−0.674589	−	0.738193i	$-0.735679\pi$
$827$	3.74060	−	4.15436i	0.130074	−	0.144461i	0.804663	+	0.593732i	$0.202346\pi$
$828$		0			0
$829$	3.23508	+	30.7797i	0.112359	+	1.06902i	0.894852	+	0.446363i	$0.147281\pi$
$829$	3.23508	+	30.7797i	0.112359	+	1.06902i	−0.782493	+	0.622659i	$0.786052\pi$
$830$	19.1087	−	0.667291i	0.663274	−	0.0231620i
$831$		0			0
$832$	−4.53496	−	1.13069i	−0.157221	−	0.0391997i
$833$	−5.75547	−	8.53283i	−0.199415	−	0.295645i
$834$		0			0
$835$	14.1164	+	2.48911i	0.488519	+	0.0861391i
$836$	0.137344	−	0.268338i	0.00475013	−	0.00928065i
$837$		0			0
$838$	−15.5331	+	5.04701i	−0.536582	+	0.174346i
$839$	−21.3293	−	22.0872i	−0.736370	−	0.762533i	0.241803	−	0.970325i	$-0.422261\pi$
$839$	−21.3293	−	22.0872i	−0.736370	−	0.762533i	−0.978173	+	0.207792i	$0.933372\pi$
$840$		0			0
$841$	−29.8848	+	38.2508i	−1.03051	+	1.31899i
$842$	−1.91000	−	4.72741i	−0.0658229	−	0.162917i
$843$		0			0
$844$	−0.176845	+	0.616732i	−0.00608725	+	0.0212288i
$845$	−4.52550	+	21.2908i	−0.155682	+	0.732426i
$846$		0			0
$847$	−11.4972	+	2.39988i	−0.395049	+	0.0824610i
$848$	−1.35228	+	1.61158i	−0.0464375	+	0.0553420i
$849$		0			0
$850$	3.29620	−	6.75820i	0.113059	−	0.231804i
$851$	−21.3363	+	22.0944i	−0.731399	+	0.757386i
$852$		0			0
$853$	12.9075	+	20.6563i	0.441945	+	0.707259i	0.991772	−	0.128019i	$-0.0408619\pi$
$853$	12.9075	+	20.6563i	0.441945	+	0.707259i	−0.549827	+	0.835279i	$0.685306\pi$
$854$	5.50539	+	2.45116i	0.188391	+	0.0838769i
$855$		0			0
$856$	31.3304	+	6.65948i	1.07085	+	0.227616i
$857$	−19.1995	+	6.98806i	−0.655844	+	0.238708i	−0.648441	−	0.761265i	$-0.724579\pi$
$857$	−19.1995	+	6.98806i	−0.655844	+	0.238708i	−0.00740289	+	0.999973i	$0.502356\pi$
$858$		0			0
$859$	10.8737	−	9.12408i	0.371004	−	0.311310i	−0.438154	−	0.898900i	$-0.644368\pi$
$859$	10.8737	−	9.12408i	0.371004	−	0.311310i	0.809159	+	0.587590i	$0.199923\pi$
$860$	2.00704	−	57.4742i	0.0684396	−	1.95985i
$861$		0			0
$862$	−1.50448	−	3.08465i	−0.0512430	−	0.105064i
$863$	−18.3231	−	5.95354i	−0.623726	−	0.202661i	−0.0199320	−	0.999801i	$-0.506345\pi$
$863$	−18.3231	−	5.95354i	−0.623726	−	0.202661i	−0.603794	+	0.797141i	$0.706345\pi$
$864$		0			0
$865$	36.6396	+	50.4301i	1.24579	+	1.71468i
$866$	−1.44643	+	1.39680i	−0.0491518	+	0.0474653i
$867$		0			0
$868$	1.24993	−	3.43415i	0.0424254	−	0.116563i
$869$	−6.33880	+	3.79297i	−0.215029	+	0.128668i
$870$		0			0
$871$	5.06843	−	3.95989i	0.171737	−	0.134176i
$872$	15.5039	+	34.8222i	0.525027	+	1.17923i
$873$		0			0
$874$	−0.237283	+	0.0504361i	−0.00802623	+	0.00170603i
$875$	−9.39234	+	5.86898i	−0.317519	+	0.198408i
$876$		0			0
$877$	16.4549	+	8.02559i	0.555642	+	0.271005i	0.694724	−	0.719276i	$-0.255526\pi$
$877$	16.4549	+	8.02559i	0.555642	+	0.271005i	−0.139082	+	0.990281i	$0.544415\pi$
$878$	1.12830	+	2.12202i	0.0380782	+	0.0716146i
$879$		0			0
$880$	26.9047	+	6.26329i	0.906957	+	0.211136i
$881$	−8.38112	+	4.83884i	−0.282367	+	0.163025i	−0.634494	−	0.772927i	$-0.718792\pi$
$881$	−8.38112	+	4.83884i	−0.282367	+	0.163025i	0.352127	+	0.935952i	$0.385458\pi$
$882$		0			0
$883$	−35.1830	+	15.6645i	−1.18400	+	0.527151i	−0.901779	−	0.432198i	$-0.857738\pi$
$883$	−35.1830	+	15.6645i	−1.18400	+	0.527151i	−0.282222	+	0.959349i	$0.591071\pi$
$884$	−6.54113	−	4.41205i	−0.220002	−	0.148393i
$885$		0			0
$886$	13.6296	−	5.50671i	0.457895	−	0.185002i
$887$	−4.32739	+	1.24086i	−0.145299	+	0.0416639i	−0.347499	−	0.937680i	$-0.612969\pi$
$887$	−4.32739	+	1.24086i	−0.145299	+	0.0416639i	0.202199	+	0.979344i	$0.435191\pi$
$888$		0			0
$889$	1.76550	−	0.248125i	0.0592130	−	0.00832184i
$890$	−19.4468			−0.651858
$891$		0			0
$892$	−0.0756542			−0.00253309
$893$	−0.0303517	+	0.00426565i	−0.00101568	+	0.000142745i
$894$		0			0
$895$	−41.7949	+	11.9845i	−1.39705	+	0.400597i
$896$	−11.4084	+	4.60929i	−0.381127	+	0.153985i
$897$		0			0
$898$	−17.7955	−	12.0032i	−0.593844	−	0.400553i
$899$	16.1438	−	7.18770i	0.538427	−	0.239723i
$900$		0			0
$901$	−1.37935	+	0.796371i	−0.0459530	+	0.0265310i
$902$	19.4880	−	1.66906i	0.648878	−	0.0555737i
$903$		0			0
$904$	−4.45201	−	8.37302i	−0.148072	−	0.278482i
$905$	18.8736	+	9.20525i	0.627379	+	0.305993i
$906$		0			0
$907$	−27.0709	+	16.9158i	−0.898875	+	0.561680i	−0.898819	−	0.438320i	$-0.855574\pi$
$907$	−27.0709	+	16.9158i	−0.898875	+	0.561680i	−5.63944e−5		1.00000i	$0.500018\pi$
$908$	−14.1146	+	3.00015i	−0.468409	+	0.0995635i
$909$		0			0
$910$	−2.22839	−	5.00505i	−0.0738705	−	0.165916i
$911$	−24.0466	+	18.7873i	−0.796699	+	0.622450i	−0.929554	−	0.368686i	$-0.879808\pi$
$911$	−24.0466	+	18.7873i	−0.796699	+	0.622450i	0.132855	+	0.991136i	$0.457586\pi$
$912$		0			0
$913$	−2.89633	+	32.4221i	−0.0958546	+	1.07301i
$914$	−2.19975	+	6.04376i	−0.0727613	+	0.199910i
$915$		0			0
$916$	−11.1281	+	10.7463i	−0.367683	+	0.355068i
$917$	5.03661	+	6.93230i	0.166324	+	0.228925i
$918$		0			0
$919$	−13.3016	−	4.32196i	−0.438780	−	0.142568i	0.0812927	−	0.996690i	$-0.474095\pi$
$919$	−13.3016	−	4.32196i	−0.438780	−	0.142568i	−0.520073	+	0.854122i	$0.674095\pi$
$920$	−26.5474	−	54.4302i	−0.875240	−	1.79451i
$921$		0			0
$922$	−0.0155197	+	0.444427i	−0.000511115	+	0.0146364i
$923$	5.08773	−	4.26911i	0.167465	−	0.140519i
$924$		0			0
$925$	−27.1435	+	9.87941i	−0.892472	+	0.324833i
$926$	0.354143	+	0.0752754i	0.0116379	+	0.00247370i
$927$		0			0
$928$	−42.4783	−	18.9126i	−1.39442	−	0.620835i
$929$	9.42952	+	15.0904i	0.309372	+	0.495099i	0.965799	−	0.259290i	$-0.0834886\pi$
$929$	9.42952	+	15.0904i	0.309372	+	0.495099i	−0.656427	+	0.754389i	$0.727933\pi$
$930$		0			0
$931$	−0.216927	+	0.224634i	−0.00710950	+	0.00736210i
$932$	8.75990	−	17.9605i	0.286940	−	0.588315i
$933$		0			0
$934$	7.03450	−	8.38339i	0.230176	−	0.274313i
$935$	17.5190	+	11.4226i	0.572932	+	0.373558i
$936$		0			0
$937$	5.54827	−	26.1026i	0.181254	−	0.852734i	−0.789705	−	0.613487i	$-0.789766\pi$
$937$	5.54827	−	26.1026i	0.181254	−	0.852734i	0.970959	−	0.239247i	$-0.0769005\pi$
$938$	0.389997	−	1.36008i	0.0127339	−	0.0444082i
$939$		0			0
$940$	−1.31927	−	3.26530i	−0.0430297	−	0.106502i
$941$	4.60346	−	5.89216i	0.150068	−	0.192079i	−0.707102	−	0.707111i	$-0.749998\pi$
$941$	4.60346	−	5.89216i	0.150068	−	0.192079i	0.857171	+	0.515033i	$0.172220\pi$
$942$		0			0
$943$	63.3312	+	65.5814i	2.06235	+	2.13562i
$944$	17.4773	−	5.67873i	0.568839	−	0.184827i
$945$		0			0
$946$	−16.6903	−	2.67479i	−0.542649	−	0.0869649i
$947$	23.6490	+	4.16996i	0.768490	+	0.135505i	0.544130	−	0.839001i	$-0.316860\pi$
$947$	23.6490	+	4.16996i	0.768490	+	0.135505i	0.224360	+	0.974506i	$0.427971\pi$
$948$		0			0
$949$	−13.4771	−	19.9807i	−0.437486	−	0.648599i
$950$	−0.221360	−	0.0551912i	−0.00718185	−	0.00179064i
$951$		0			0
$952$	−3.76865	+	0.131604i	−0.122143	+	0.00426531i
$953$	0.246283	+	2.34323i	0.00797790	+	0.0759046i	0.997786	−	0.0665000i	$-0.0211832\pi$
$953$	0.246283	+	2.34323i	0.00797790	+	0.0759046i	−0.989809	+	0.142405i	$0.954517\pi$
$954$		0			0
$955$	−12.2884	+	13.6477i	−0.397644	+	0.441629i
$956$	−22.0064	−	18.4656i	−0.711739	−	0.597220i
$957$		0			0
$958$	0.776331	+	4.40279i	0.0250821	+	0.142248i
$959$	−16.9347	+	9.00435i	−0.546850	+	0.290765i
$960$		0			0
$961$	26.9069	+	1.88152i	0.867965	+	0.0606941i
$962$	−1.08800	−	5.11864i	−0.0350786	−	0.165032i
$963$		0			0
$964$	7.20495	−	0.757271i	0.232056	−	0.0243901i
$965$	−66.2834	−	19.0064i	−2.13374	−	0.611839i
$966$		0			0
$967$	−33.9891	−	40.5066i	−1.09302	−	1.30261i	−0.949780	−	0.312917i	$-0.898694\pi$
$967$	−33.9891	−	40.5066i	−1.09302	−	1.30261i	−0.143236	−	0.989689i	$-0.545751\pi$
$968$	7.64098	−	20.7568i	0.245590	−	0.667150i
$969$		0			0
$970$	−1.76050	−	12.5266i	−0.0565264	−	0.402206i
$971$	−25.6769	+	35.3412i	−0.824011	+	1.13415i	0.164997	+	0.986294i	$0.447239\pi$
$971$	−25.6769	+	35.3412i	−0.824011	+	1.13415i	−0.989008	+	0.147860i	$0.952761\pi$
$972$		0			0
$973$	6.77547	−	20.8528i	0.217212	−	0.668509i
$974$	16.7090	+	8.88432i	0.535390	+	0.284672i
$975$		0			0
$976$	20.0049	−	13.4935i	0.640342	−	0.431916i
$977$	−22.7204	+	36.3603i	−0.726891	+	1.16327i	0.253715	+	0.967279i	$0.418347\pi$
$977$	−22.7204	+	36.3603i	−0.726891	+	1.16327i	−0.980606	+	0.195990i	$0.937208\pi$
$978$		0			0
$979$	4.09481	−	32.8527i	0.130871	−	1.04998i
$980$	−31.0742	−	17.9407i	−0.992629	−	0.573095i
$981$		0			0
$982$	−0.273441	+	2.60162i	−0.00872585	+	0.0830209i
$983$	0.608144	−	8.69687i	0.0193968	−	0.277387i	−0.978177	−	0.207772i	$-0.933379\pi$
$983$	0.608144	−	8.69687i	0.0193968	−	0.277387i	0.997574	−	0.0696145i	$-0.0221769\pi$
$984$		0			0
$985$	−5.18492	+	36.8927i	−0.165205	+	1.17550i
$986$	−6.03722	−	5.83008i	−0.192264	−	0.185668i
$987$		0			0
$988$	−0.0896762	+	0.221956i	−0.00285298	+	0.00706137i
$989$	−39.3944	−	68.2330i	−1.25267	−	2.16968i
$990$		0			0
$991$	6.37882	−	11.0484i	0.202630	−	0.350965i	−0.746745	−	0.665110i	$-0.768385\pi$
$991$	6.37882	−	11.0484i	0.202630	−	0.350965i	0.949375	+	0.314145i	$0.101718\pi$
$992$	6.52416	+	8.35054i	0.207142	+	0.265130i
$993$		0			0
$994$	0.353449	−	1.41761i	0.0112107	−	0.0449638i
$995$	74.6670	+	58.3362i	2.36710	+	1.84938i
$996$		0			0
$997$	−1.39044	+	0.678161i	−0.0440356	+	0.0214776i	−0.460257	−	0.887786i	$-0.652243\pi$
$997$	−1.39044	+	0.678161i	−0.0440356	+	0.0214776i	0.416222	+	0.909263i	$0.363354\pi$
$998$	8.50841	+	6.18172i	0.269329	+	0.195679i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.bb.a.413.20		816
3.2	odd	2		297.2.x.a.83.15	yes	816
11.2	odd	10	inner	891.2.bb.a.332.20		816
27.13	even	9		297.2.x.a.149.15	yes	816
27.14	odd	18	inner	891.2.bb.a.314.20		816
33.2	even	10		297.2.x.a.2.15	✓	816
297.13	odd	90		297.2.x.a.68.15	yes	816
297.68	even	90	inner	891.2.bb.a.233.20		816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.2.15	✓	816	33.2	even	10
297.2.x.a.68.15	yes	816	297.13	odd	90
297.2.x.a.83.15	yes	816	3.2	odd	2
297.2.x.a.149.15	yes	816	27.13	even	9
891.2.bb.a.233.20		816	297.68	even	90	inner
891.2.bb.a.314.20		816	27.14	odd	18	inner
891.2.bb.a.332.20		816	11.2	odd	10	inner
891.2.bb.a.413.20		816	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.bb (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.537360 - 0.0755211i) q^{2} +(-1.63947 + 0.470111i) q^{4} +(-3.32873 + 1.34490i) q^{5} +(0.885188 + 0.597067i) q^{7} +(-1.83694 + 0.817857i) q^{8} +(-1.68716 + 0.974083i) q^{10} +(-1.29032 - 3.05533i) q^{11} +(1.23652 + 2.32555i) q^{13} +(0.520756 + 0.253990i) q^{14} +(1.96743 - 1.22939i) q^{16} +(1.71802 - 0.365177i) q^{17} +(-0.0216751 - 0.0486831i) q^{19} +(4.82511 - 3.76979i) q^{20} +(-0.924110 - 1.54437i) q^{22} +(2.86915 - 7.88293i) q^{23} +(5.67502 - 5.48030i) q^{25} +(0.840084 + 1.15628i) q^{26} +(-1.73193 - 0.562737i) q^{28} +(-3.86018 - 7.91454i) q^{29} +(-0.0700374 + 2.00561i) q^{31} +(4.04507 - 3.39421i) q^{32} +(0.895619 - 0.325979i) q^{34} +(-3.74955 - 0.796991i) q^{35} +(-3.34485 - 1.48922i) q^{37} +(-0.0153239 - 0.0245234i) q^{38} +(5.01474 - 5.19292i) q^{40} +(-4.76416 + 9.76798i) q^{41} +(6.03712 - 7.19476i) q^{43} +(3.55179 + 4.40254i) q^{44} +(0.946441 - 4.45265i) q^{46} +(0.158533 - 0.552870i) q^{47} +(-2.19518 - 5.43326i) q^{49} +(2.63565 - 3.37348i) q^{50} +(-3.12050 - 3.23138i) q^{52} +(-0.862436 + 0.280222i) q^{53} +(8.40424 + 8.43504i) q^{55} +(-2.11435 - 0.372817i) q^{56} +(-2.67202 - 3.96143i) q^{58} +(7.68590 + 1.91631i) q^{59} +(10.3949 - 0.362997i) q^{61} +(0.113830 + 1.08302i) q^{62} +(-1.18738 + 1.31871i) q^{64} +(-7.24367 - 6.07816i) q^{65} +(-0.424053 - 2.40492i) q^{67} +(-2.64498 + 1.40636i) q^{68} +(-2.07505 - 0.145101i) q^{70} +(-0.524273 - 2.46651i) q^{71} +(-9.10036 + 0.956486i) q^{73} +(-1.90986 - 0.547642i) q^{74} +(0.0584222 + 0.0696248i) q^{76} +(0.682061 - 3.47495i) q^{77} +(-0.309973 - 2.20558i) q^{79} +(-4.89565 + 6.73828i) q^{80} +(-1.82238 + 5.60872i) q^{82} +(-8.66574 - 4.60765i) q^{83} +(-5.22772 + 3.52614i) q^{85} +(2.70075 - 4.32211i) q^{86} +(4.86907 + 4.55716i) q^{88} +(8.64475 + 4.99105i) q^{89} +(-0.293959 + 2.79684i) q^{91} +(-0.998041 + 14.2727i) q^{92} +(0.0434360 - 0.309063i) q^{94} +(0.137624 + 0.132902i) q^{95} +(-2.43238 + 6.02035i) q^{97} +(-1.58993 - 2.75383i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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